Have a lovely old, dark oak dining table, and has a white water mark (from vase!) on it. Don't really want to sand it, but how do you colour this mark?

If the wood is real oak and the finish is old varnish or shellac, I would rub with a tiny bit of spirits on a cotton ball or Q tip. Alcohol, paint thinner, turpentine, etc. It will disburse the finish over the white area. To even it out afterwards you could apply butcher wax and rub to a uniform sheen again. There might already be wax on the table, so what happens depends a lot on what exactly is on the table to begin with.